A natural direction for future work is to generalize to subregions without reflection symmetry. Then the techniques used here do not apply since reflection symmetry guarantees that the tip of the HRT surface stays at the same boundary coordinates as \(R\)  is varied. This in turn allows for the Hamilton-Jacobi argument at the beginning of section  that relates \(\frac{dA}{dR}\)  to the near-boundary behavior of the HRT surface. In the absence of reflection symmetry, we need a more general technique, perhaps a “matching technique” similar to the one used in [1]}, [2]}.
